{"status": "success", "data": {"description_md": "Integers $a, b, c,$ and $d$, not necessarily distinct, are chosen independently and at random from 0 to 2007, inclusive. What is the probability that $ad-bc$ is even?\n\n$\\mathrm{(A)}\\ \\frac 38\\qquad \\mathrm{(B)}\\ \\frac 7{16}\\qquad \\mathrm{(C)}\\ \\frac 12\\qquad \\mathrm{(D)}\\ \\frac 9{16}\\qquad \\mathrm{(E)}\\ \\frac 58$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Integers <span class=\"katex--inline\">a, b, c,</span> and <span class=\"katex--inline\">d</span>, not necessarily distinct, are chosen independently and at random from 0 to 2007, inclusive. What is the probability that <span class=\"katex--inline\">ad-bc</span> is even?</p>&#10;<p><span class=\"katex--inline\">\\mathrm{(A)}\\ \\frac 38\\qquad \\mathrm{(B)}\\ \\frac 7{16}\\qquad \\mathrm{(C)}\\ \\frac 12\\qquad \\mathrm{(D)}\\ \\frac 9{16}\\qquad \\mathrm{(E)}\\ \\frac 58</span></p>&#10;<hr/>&#10;<p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2007 AMC 12A Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/07_amc12A_p13", "prev": "/problem/07_amc12A_p11"}}